4 RRI Pipeline
rri_pipeline() integrates available observed domains
into an exploratory composite. The simulator’s hidden architecture
columns are excluded. We use explicit measured anchors to orient
otherwise arbitrary PCA axes.
rri_out <- rri_pipeline(
plant = sim$ROS_flux,
soil = sim$Eh_stability,
micro = log1p(sim$micro_gene_abundance),
id = sim$id,
mode = "snapshot",
scaling = "pnorm",
direction_anchor_phys = "FvFm",
direction_anchor_soil = "Eh",
direction_anchor_micro = "mtrA",
domain_weights = c(Physio=0.35, Soil=0.40, Micro=0.25)
)
## Align once and reuse this identifier-complete table downstream.
rri_scored <- attach_hrri_ids(rri_out$row_scores, sim$id)
attr(rri_scored, "id_alignment")
#> [1] "observation keys"
summary(rri_scored$RRI)
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> 0.2247 0.3866 0.5125 0.5126 0.6417 0.8091
head(rri_scored[, c("plot", "depth", "plant_id", "time",
"RRI", "Physio", "Soil", "Micro")])
#> plot depth plant_id time RRI Physio Soil Micro
#> 1 P1 D1 Plant1 1 0.5331287 0.4047907 0.8681722 0.1767324
#> 2 P2 D1 Plant1 1 0.6660409 0.4460895 0.7806314 0.7906280
#> 3 P1 D2 Plant1 1 0.4499651 0.4141672 0.2643849 0.7970104
#> 4 P2 D2 Plant1 1 0.4119487 0.5263208 0.1609431 0.6534366
#> 5 P1 D1 Plant2 1 0.6296590 0.4048218 0.8278830 0.6272726
#> 6 P2 D1 Plant2 1 0.5933279 0.4741678 0.8424479 0.3615599Alignment uses complete observation keys, or a shared unique
row_id when available. If neither is returned the pipeline
must preserve input row order — matching row counts alone do
not establish alignment. Shared identifier columns are
checked for conflicts rather than silently overwritten.
4.1 Agreement with the prescribed target
A single pooled correlation is the wrong summary here, for two reasons.
First, these 360 rows are 12 trajectories observed at 30 time points, not 360 independent observations. Rows within a trajectory are strongly dependent, so an interval computed from the row count is far too narrow.
Second, Pearson’s \(r\) measures association, not agreement. A score equal to twice the target plus a constant correlates with it perfectly while matching it nowhere. Lin’s concordance correlation coefficient penalises departure from the 1:1 line and is the quantity that belongs beside it.
rri_accuracy() reports both, with intervals obtained by
resampling whole trajectories rather than rows.
## rri_scored is aligned to sim$id, and hence to its latent_truth vector.
truth <- sim$latent_truth
if (!is.numeric(truth) || length(truth) != nrow(rri_scored)) {
stop("latent_truth must be a numeric vector with one value per sim$id row.")
}
## One independent experimental unit = one plot x depth x plant trajectory.
traj <- interaction(rri_scored$plot, rri_scored$depth, rri_scored$plant_id,
drop = TRUE)
acc <- rri_accuracy(
score = rri_scored$RRI,
target = truth,
cluster = traj,
n_boot = 500,
n_perm = 500,
seed = 42
)
acc
#> Agreement with reference target
#> --------------------------------------------------------------
#> statistic row_level cluster_mean_level ci_lower ci_upper
#> pearson_r 0.4668 0.5454 0.3037 0.5959
#> lins_ccc 0.1412 0.0782 0.0829 0.2147
#> rmse 0.1732 0.1631 0.1296 0.2052
#> mae 0.1415 0.1264 0.0971 0.1836
#> bias -0.1124 -0.1124 -0.1688 -0.0497
#> r2 -21.5196 -98.0483 -34.2773 -14.7249
#>
#> Dependence structure
#> 360 observations in 12 clusters (mean size 30.0)
#> ICC 0.768, design effect 23.3, effective n 15
#>
#> Error decomposition (percent of MSE)
#> squared_bias 42.1%
#> variance_mismatch 39.1%
#> lack_of_correlation 18.8%
#>
#> Calibration: target = 0.565 + 0.118 x score (ideal 0 and 1)
#> Cluster permutation test: p = 0.0220 (500 permutations)
#>
#> Notes
#> Rows are strongly clustered (ICC 0.77, design effect 23.3). The 360
#> observations carry roughly the information of 15 independent ones; quote
#> the cluster bootstrap interval, not one based on n = 360.
#> Ignoring clustering would give a 95% interval for r of width 0.145;
#> resampling whole trajectories gives width 0.292, 2.0 times wider. Report
#> the latter.
#> Correlation (0.467) exceeds concordance (0.141). The score tracks the
#> target's pattern but does not agree with it in level or scale; see
#> calibration.
#> Calibration slope is 0.12 rather than 1: the score compresses or
#> exaggerates the target's range.
#> R2 is negative: as an absolute predictor the score does worse than the
#> target's own mean. It may still rank correctly; check pearson_r.
#> Error is dominated by squared_bias (42% of MSE).
#> If score and target derive from the same generator, this is internal
#> consistency, not validation.effective_n in the dependence table, not the row count,
is what governs precision. Where the design effect is well above one,
the naive interval should not be quoted: the function prints both widths
so the difference is visible rather than asserted.
Splitting the error says which kind of disagreement is present, and the three components sum to the mean squared error exactly.
acc$decomposition[, c("component", "percent")]
#> component percent
#> 1 squared_bias 42.10174
#> 2 variance_mismatch 39.10814
#> 3 lack_of_correlation 18.79012
## Exactness check: the residual is numerical noise, not a rounding allowance.
c(mse = attr(acc$decomposition, "mse"),
residual = attr(acc$decomposition, "residual"))
#> mse residual
#> 3.000571e-02 -1.040834e-17Large squared bias is a systematic offset, removable by recentring. Large variance mismatch means the score is flatter or more volatile than the target. Large lack of correlation means the score does not track the target’s pattern, and no rescaling will repair it.
plot_rri_accuracy() draws the same four questions as one
figure.
Reading it. A puts the fitted line against the dashed 1:1 line; a flatter fit means the score compresses the target’s range. Open points are trajectory means, the level at which the units are independent. B is a Bland-Altman plot: a scatter that slopes or fans out shows disagreement that depends on level, which no correlation coefficient can reveal. C is the headline: the violet distribution resamples rows and is too narrow, the teal one resamples trajectories and is honest; the bars beneath give both widths. D partitions the mean squared error exactly.
What it does not show. None of the four panels speaks to out-of-sample performance. The target is prescribed by the same simulator that produced the inputs, so a tight panel A means the estimator is self-consistent, not that it would recover an unobserved field quantity.
latent_truth and RRI are produced by the
same generator. Everything above therefore quantifies internal
consistency — whether the estimator recovers the target its own
simulator prescribed. It is not independent predictive validation, and
it is not evidence that the individual latent parameters have been
identified. An empirical claim requires a target measured independently
of the score, replicated across independent experimental units.